Musical tone wave shape generating apparatus

ABSTRACT

D R A W I N G A first memory digitally stores the levels of the spectra of the fundamental wave and each harmonic up to the mth harmonic of intended tone color waves, a second memory digitally stores values XO through XN of a sinusoidal wave function at the respective points in its one cycle sampled by a sampling number N, and a third memory is for writing incoming information to be thereafter read out. Digital signals (a, b, . . . z) each representing amplitude of the respective tone color are sequentially and repetitiously produced. The levels of the spectra (fundamentals: a1b1, . . . z1; second harmonics: a2, b2 . . . z2; . . . ; mth harmonics: am, bm, . . . zm) for the respective tone color waves are sequentially read from the first memory. The amplitude signals and the level signals are respectively multiplied with each other tone color by tone color, and thereafter are added cumulatively for each of the fundamental waves and the harmonics to produce each cumulative value Hp (a X ap) + (b X bp) + . . . + (z X zp); where p . . . ,m. On the other hand, values of the sinusoidal function at the respective address points PQ mod N, where Q 1, . . . N, are read from the second memory and these read out outputs are multiplied by the respective value Hp. The products of the multiplication are added cumulatively for values H1 through Hm to obtain a signal

United States Patent [191 1111 3,823,390 Tomisawa et a1. July 9, 1974 MUSICAL TONE WAVE SHAPE [57] ABSTRACT GENERATING APPARATUS A first memory digitally stores the levels of the spectra 75 lnvemors; Norio Tomisawa, Hamamatsu; of the fundamental wave and each harmonic up to the Y ji U hi H ki mth harmomc of intended tone color waves, a second Takamshi o Toshjo memory digitally stores values X through X of a si- Takeda, both f Hamamatsu, n f nusoidal wave function at the respective points in its Japan one cycle sampled by a sampling number N, and a third memory is for writing incoming information to [73] Asslgnee: 'Q l Kabushlkl be thereafter read out. Digital signals (a, b, z) each Kmsha sh'zuokenken Japan representing amplitude of the respective tone color 22 Fil d; J 15, 1973 are sequentially and repetitiously produced. The levels of the spectra (fundamentals: a b 1,; second har- [211 Appl' 3232609 monics: a b Z2, mth harmonics: a,,,, b,,,, z,,,) for the respective tone color waves are sequen- 30] F i A li i P i i D m tiallly regdg'rolm the first] memory. The arlnplitulde fig;

nas an t e eve signas are respective y mu t1p 1e Jan. 17, 1972 Japan 47 6757 with each other tone color by tone Color, and thereaf- U-S tel are added cumulatively for each of the fundamen- [5 I lnL'Cl. n WaVS and the harmonics [O pl'OdUCfi eflCh cumula- [58] Field of Search 340/1725; 84/1.01, 1.02, Value (a X 111+(b X bp) (Z X 84/103, 128' 345, DIG. 29, L27 wherep ,m. On the other hand, values of the s1- nusoldal functlon at the respective address pomts PQ [56] References Cited mod N, where Q l, N, are read from the second memory and these read out outputs are multiplied by UNITED STATES PATENTS the respective value H The products of the multiplication are added cumulatively for values H through a son 3,639,913 2/1972 Watson .1 340/1725 Hm to Obtain a Sgnal 3,659.488 5/1972 Deutsch.... 84/345 m 3,696,201 10/1972 Arsem n 84/].01 3,697,661 10/1972 Deutsch 3.733.593 5/1973 Molnar 340/1725 a ,AWLM, ifime OTHER PUBLICATIONS Digital Transversal Filter With Read-Only Memory," IBM Technical Disclosure Bulletin, Vol. 15, No. 3, August 1972, pp. 976-977.

Primary ExaminerPaul .l. Henon Assistant Examiner.lames D. Thomas Attorney, Agent, or Firm-Ladas, Parry, Von Gehr,

Goldsmith & Deschamps This signal Y is sequentially written in an address Q in the third memory to constitute the desired musical tone wave shape. Then this musical tone wave shape is read out at an appropriate rate.

9 Claims, 5 Drawing Figures PATENTED 91974 3.823.390

sum a 0:- 4

FIG. lb

PATENTED UL 3. 823.390

sum 30F 4 TONE COLOR A TONE COLOR B PATENTED JUL 9 I974 SHEET t F 4 FIG.3

MUSICAL TONE WAVE SHAPE GENERATING APPARATUS This invention relates to a musical tone wave shape generating apparatus.

A musical tone wave shape can be divided into a fundamental wave content and one or more harmonic contents, no matter how complicated the wave shape may appear. Conversely, a desired musical tone wave shape can be obtained by synthesizing its fundamental wave and one or more predetermined harmonics at an appropriate ratio of levels. The present invention makes use of this principle.

A specific musical tone wave shape may be obtained by providing a memory which stores this specific musical tone wave shape and reading it from the memory. It is very difficult, however, to change the contents once stored in the memory. ln order to obtain a plurality of different musical tone wave shapes, it is therefore necessary to provide a plurality of memories which respectively store one of the different wave shapes. If the number of required musical tone wave shapes is large, a corresponding large number of memories are required. Furthermore, a desired musical tone wave shape will not always be obtained from one of these memories if the desired wave shape is not stored in any of the memories.

For obtaining a musical tone wave shape, it is also possible to provide memories which respectively store the fundamental wave and each hamionic, read these waves from the respective memories and synthesize them at a suitable ratio of levels. This alternative, however, is still not quite free from the disadvantage that the apparatus requires a large number of memories.

It is. therefore, a general object of the invention to provide a musical tone wave shape generating apparatus capable of producing a desired musical tone wave shape with a relatively simple construction.

It is another object of the invention to provide a musical tone wave shape generating apparatus capable of producing a desired musical tone wave shape by providing a single memory storing sinusoidal waves in digital representation, reading the fundamental wave and each harmonic of the desired musical tone wave shape from this single memory and synthesizing these waves at an appropriate ratio of levels into the desired musical tone wave shape.

lt is another object of the invention to provide a musical tone wave shape generating apparatus which comprises means for determining amplitudes of a plurality of tone-colors, a first memory for storing digitally the levels of spectra of each tone-color, a first addition circuit for multiplying the spectra of the fundamental wave and harmonics of each tone-color with corresponding volumes and adding the products of the multiplication for each of the fundamental wave and harmonics. a second memory for storing digitally the sinusoidal wave shape of the fundamental wave shape for one cycle, means for providing readout address signals to said second memory in a predetermined order and thereby reading out each function value of the fundamental wave and harmonics, a second addition circuit for multiplying the signals read from the second memory with the signals from the first addition circuit and adding the products of the multiplication each time the signal corresponding either to the fundamental wave or the highest harmonic is produced from the first addi- 2 tion circuit, means for writing in time sequence digital signals representing the results of the addition from the second addition circuit into a third memory and means for reading out the contents of the third memory at a predetermined clock rate.

It is still another object of the invention to provide a musical tone wave shape generating apparatus which is capable of converting an analog signal representing the amplitude of each tone-color to a digital signal by providing a single analog-to-digital converter.

Other objects and features of the invention will become apparent from the description made hereinbelow with reference to the accompanying drawings in which:

FIGS. la and lb are block diagrams showing one embodiment of the musical tone wave shape generating apparatus according to the invention. The circuit of this embodiment is divided into two parts by line I-l;

FIG. 2a is a graphical diagram showing the wave shape of an input to an analog-to-digital converter;

FIG. 2b is a graphical diagram showing the levels of spectra of each tone-color;

FIG. 3 is a graphical diagram for illustrating the reading from a sinusoidal wave function memory;

FIG. 4 is a diagram showing one example of a wave shape stored in a composite wave shape memory CM.

FIG. 1 is a block diagram illustrating one embodiment of the musical tone wave shape generating apparatus according to the invention. Clock pulses from a clock pulse generator C, are applied to a tone-color scanning counter TC. The tone-color scanning counter TC consists, for example, of flip-flops of five stages. The output of each flip-flop is applied to a decoder D The decoder D, successively produces its outputs (e.g., negative pulses) A through Z, A in accordance with the contents of the counter TC, producing outputs in a manner similar to a ring counter.

There are provided tone-color selection and control knobs So to 82 corresponding respectively to tone colors A to Z. The amplitude of a selected tone color can be controlled by operating a corresponding knob. Amplitude control devices VR, to VR, consists, for example, of variable resistors each slider of which is operable by the knob.

Each slider of the amplitude control devices is connected to the drain of corresponding transistors TR, to TR, which respectively constitute gate circuits. The sources of these transistors TR, to TR, are connected in common connection to the input tenninal of an analog-to-digital converter AD. The gates of the transistors TR to TR, are respectively connected to the output terminals of the decoder D,.

When the decoder D, is actuated to successively produce its outputs A, B, Z, A, B the transistors of the gate circuit successively and cyclicly conduct in the order of TR TR, TR,, TR, If the tonecolor selection and control knobs Sa to 82: are respectively set at predetermined positions, voltages corresponding to the set positions of these knobs are successively applied to the input of the analog-to-digital converter AD. These applied voltages constitute a wave shape such as shown in FIG. 2a where voltage a corresponds to the knob S voltage b to the knob S and voltage 2 to the knob S, respectively. These voltages are converted in the analog-to-digital converter AD to digital signals consisting of a suitable bit number, e.g., and thereafter applied to the input terminals on one side of a multiplication circuit ML,.

The output of the last stage of the scanning counter TC is applied to a harmonic scanning counter HC. The harmonic scanning counter HC consists, for example, of flip-flops of five stages the outputs of which are applied to a decoder D The decoder D, successively produces outputs l, 2, 32, l, in accordance with the contents of the scanning counter HC. Each of these outputs is used for designating a specific column of a tone-color spectra memory RM.

The tone-color spectra memory RM consists, for example, of a read only memory (ROM) and stores the levels of a fundamental wave component and higher harmonic wave components of each tone-color A, B, C, 2. Each component of the tone-colors A through Z (hereinafter called spectrum") has a level such as shown in FIG. 2b. In FIG. 2b, small letters a, b, c, 1 respectively represent the components of the tonecolours A, B, C Z. The numeral 1 affixed to these small letters represents the fundamental wave, the numeral 2 the second hannonic, and the numeral 32 the 32nd harmonic respectively. Accordingly, a,, for example, represents the level of the fundamental wave component of the tone-color A.

The spectra a, through a b, through b;,,, 2, through 2,, are respectively stored in the tone-color spectra memory RM as digital information. The spectra a, through 0 b, through bag; z, through 2 are respectively stored in each row. Hence, the spectra a,, b, z, are stored in the first column, the spectra a,,, b z, in the second column and the spectra 0 b 2 in the 32nd column.

Each output line of the decoder D, is connected also to the tone-color spectra memory RM, and each output of the decoder D, selects a row of specific information stored in the memory RM. More specifically, when the output A is produced from the decoder D,, the row of the spectra 0,, 0,, a is selected by this output A,

whereas when the output 1 is produced from the decoder D,, the first column is selected by this output l. Hence the spectrum a, is read out.

As the decoder D, operates to produce the outputs A, B, Z, A, successively and repetitively, the i column selecting signal from the decoder D is shifted to a next column at each cycle of the operation of the decoder D,. Accordingly. the spectra are successively and repetitiously read from the tone-color spectra memory RM in the order of a,, b,, through z,; a,, b, through 1,; a 1),, through z Zn; 0,, b, These spectra are read out in the form of digital information consisting of a suitable number of bits, e.g., 8, and are applied to the input terminals on the other side of the multiplication circuit ML,.

When the decoder D, produces the output A, a signal a is applied through the analog-to-digital converter AD to one of said input terminals on one side of the multiplication circuit ML, and the signal a, is applied from the tone-color spectra memory RM to one of said input terminals on the other side of the circuit ML,. Consequently, the multiplication circuit ML, effects the calculation a X a, (a times a,) and provides the result of the calculation to an addition circuit AC,. When the decoder D, produces the output B, the multiplication circuit ML, likewise effects the calculation b X 12,, providing the result to the addition circuit AC,. Subsequently, results of calculations c X c,, d X d,, z X z, are provided to the addition circuit AC,. The addition circuit AC, cumulatively adds the outputs of the multiplication circuit ML, successively applied thereto and is reset by the output of the last stage of the tone-color scanning counter TC at each cycle of operation of the decoder D,. Accordingly, the addition circuit AC, effects the following calculation and thereafter is reset:

As the decoder D, completes one cycle of its operation and starts a next cycle, the decoder D produces the output 2. The multiplication circuit ML, effects calculations a X a,, b X b 0 X 0,. z X 2 in the same operation principle as has been described above. The addition circuit AC, effects the following calculation and thereafter is reset:

The addition circuit AC, subsequently makes the following calculations:

The signals H, through H are successively applied to a temporary memory HM where they are stored temporarily and thereafter are successively applied to the input terminals on one side of a multiplication circuit ML,

These signals H, through H are signals which are produced from both the amplitudes of the tone-color selection and control knobs and the levels of the spectra. The signal H, represents the level of the fundamental wave of a combined resultant musical tone wave shape to be obtained. The signal H represents the level of the second harmonic of the musical tone wave shape. Similarly, the other signals H H respectively represent the levels of the third and subsequent harmonics of the musical tone wave shape.

The reference characters SM designate a sinusoidal wave function memory which consists, for example, of a read only memory (ROM). A sinusoidal wave shape of one cycle is sampled by a suitable sampling number, e.g., 64, and values of amplitudes X,,, X,, X,,;, at respective sampling points are stored in the memory SM in the form of digital information consisting of a suitable number of bits, e.g., 8.

Each wave shape amplitude is read from the memory SM by means of a device comprising a sample address scanning counter SC, a multiplication circuit ML, and a decoder D The reading of the wave shape amplitudes will be described in detail hereinbelow.

The sample address scanning counter SC consists, for example, of flip-flops of six stages. The output of the harmonic scanning counter HC is applied to the first stage of the counter SC. Each bit output of the counter SC (hereinafter referred to as a fundamental wave phase address 0.) is applied to the input tenninals on one side of the multiplication circuit ML, Each bit output of the counter HC (hereinafter referred to as a harmonic address P.) is applied to the input terminals on the other side of the multiplication circuit ML,. The multiplication circuit ML, multiplies the address P with the address Q and produces a read out address R PQ mod 64 by taking out six consecutive digits including the least significant digit and discarding the overflow outputs of more significant digits than these six multiplication circuit ML, and the addition circuit AC digits. The states of the addresses P, Q, P X Q, R, etc.. effect calculations in the same operation principle as are shown in Table l where the address P, Q, P X Q and described above Thus, the output of the addition cir- R are represented in decimal numbers only. cuit AC is represented generally by the equation Harmonic Fundamental PXQ Read out Sinusoidal Harmonic Composite address wave phase address wave level wave (P) address (R I P-Q function (HP) shape m "a M sample value (Yul I o t) 0 x H 2 O 0 X0 1 3 0 0 x., H, 4 O 0 X0 "4 Y 32 o t) X., i-i

l l l l x, H 2 2 2 x, H, 3 3 3 X, Y

32 32 32 x H, l l 2 2 2 H, 2 4 4 )4 H, 3 e 6 x, H, t Y,

32 ti t ti x}, H

1 3 3 3 x, H 2 6 6 x 2 3 9 9 x, H i Y,

l 65 63 e3 x. H 2 12s 62 x., H, 3 I89 6| x H,

. 32 l6 6 x}, H},

If the address 0 is a decimal number 0 while the ad- 32 dress P changes from 0 to 31, the products P X Q are HP'XPQ all zero and therefore the outputs R of the multiplicap tion circuit Mb, are all zero. Accordingly, the decoder D produces only the output 0 thereby selecting the ad- This 0 represents the Q Sample Value Of a p dress 0 of the sinusoidal wave function memory SM. t musical tone Wave shape to be Obtained More p The memory SM produces th i l X hi h i clfically, the sampled wave shape amplitudes of the plied to one of the input terminals on the other side of fundamental waver the e n m rllc. the 32nd the multiplication circuit ML While the address P harmonic csnbesubswnvallyreadfrom the sinusoidal changes from 1 to 32, the signals H., H H H are W function memory SM y using the above successively applied to the input terminals on one side scribed e out address R andi a Yesutti the Signals of the multiplication circuit ML iii the manner dep s s the sampled amplitudes of the composite scribed above in synchronization with the change of the musleat tone W P e e e y prodtteed address P. Thus, the multiplication circuit ML effects from t attttttloh etrelllt 'z- This be pl ined calculations HI X0, H2 X X0 I H32 X X0 and more In detail with reference to FIGS. 3(a), (b), (c) vides the results successively to an addition circuit AC and The addition circuit AC, makes the following addition In 3 the diagram Shows the flfhdamen'lal and provides the result of the addition in the form of a wavet the dlagl'am the Second hal'monlci the d18- signal having a suitable number of bits, e.g., l2 to a gram the third e and the diagram the composite wave shape memory CM to be described fourth harmonic respectwely- The harmonics higher later; than the fourth harmonic are obtained by addressing Y (I X (H, x X (H X the fundamental wave shape stored in the sinusoidal when the addition circuit Ac, has finished the calculawave function memory SM in a suitable m n Th tion of Y it is reset by an overflow output of the harhorizontal axis which is used as a time base for the secmonic scanning counter HC to prepare for a next cal- 0n h m ni Shown n is le th f th culation. fundamental wave in length for the same period of The values P X Q and R when the address Q is decitime. Likewise, the horizontal axis in FIG. 3(0) is three mal numbers 1, 2, 3 63 are shown in Table l. The times and the one in FIG. Std) four times as long as that of the fundamental wave for the same period of time.

When the address Q is O, the sinusoidal wave function X is read from the memory SM both for the fundamental wave and each harmonic. The signals H, m H are multiplied one after another with X and the products are added together to obtain the sum Y It will be understood from the foregoing that this Y is a composite signal of the fundamental wave and each harmonic at the address 0, each component wave being provided with its predetermined level.

When the address Q is I, the functions X X X X are successively read from the memory SM for the fundamental wave, second, third, fourth and thirtysecond harmonics respectively. These functions are multiplied with the signals H, through H and thereafter are added together to produce the sum signal Y,. This signal Y, is a composite signal of the fundamental wave and each harmonic at the address I, each component wave being provided with its predetermined level.

When the address Q is 2, the functions X X X X X are read from the memory SM and the sum signal Y is obtained.

Likewise, the composite signals Y;,, Y. Y are obtained as the address Q becomes 3, 4, 63.

It will be apparent from the foregoing that the signals Y through Y respectively represent composite sample values of the fundamental wave and each harmonic.

The composite wave shape memory CM which consists, for example, of a random access memory (RAM) stores the above described signals Y through Y applied from the addition circuit AC at its predetermined addresses. When the signal Y is applied from the addition circuit AC the address 0 is simultaneously applied to the decoder D Thereupon a write address output selecting the address 0 is applied from the decoder D to the memory SM to store the signal Y at the address 0. Likewise. the signals Y Y,, Y are stored in the addresses l, 2, 63.

Thus, the composite musical tone wave shape of one cycle such as shown in FIG. 4 consisting of the sample values Y through Y. is stored in the composite wave shape memory CM in the form of digital signals.

Pulses of Nf Hz (N 2", and 1' represents the frequency of the fundamental wave of the musical tone wave shape to be obtained.) are applied from a clock pulse generator C, to a counter RC of n(e.g., six) stages. Each bit output of the counter RC is applied to a decoder D which in turn applies a read out address to the composite wave shape memory CM in accordance with the contents of the counter RC. ACcordingly, as the clock pulses are applied to the counter RC, the read out addresses 0 63, 0 are applied successively and repetitively from the decoder D to the composite wave shape memory CM, whereby the signals Y Y Y Y consisting of a suitable number of bits, e.g., 12. are successively read from the memory CM and applied to a digital-analog converter DA. This converter DA is provided for converting the digital signals Y through Y to analog signals.

Thus, a musical tone wave shape which is a composite wave shape of each tone-color consisting of the spectra stored in the memory RM and provided with the amplitude determined by one of the tone-color selection and control knobs S, through 8 is taken out of an output terminal T in the foregoing embodiment, kinds of the tone-color and the sampling number of each memory have been explained only by way of example and these may of course vary according to necessity.

Further, the tone-color spectra memory RM may be constructed of a random access memory (RAM) so that spectrum information may be variably written through a suitable reading device.

What we claim is:

l. A musical tone wave shape generating apparatus comprising:

a. a first memory for digitally storing the levels of the spectra of the fundamental wave and of each harmonic up to the mth harmonic of the intended tone color waves;

b. a second memory for digitally storing values X through X of a sinusoidal wave function at respective points of a cycle sampled by sampling number c. a third memory for writing incoming information to be thereafter read out;

d. means for sequentially and repetitively producing digital signals (a, b, z) each representing the amplitude of the respective tone color;

e. means for sequentially reading out from the first memory the level of each corresponding wave spectrum of each tone color in succession at a readout rate synchronized with the rate of production of the digital signals representing the respective tone color amplitude to produce spectral level signals (fundamentals a,, b,, 2,; second harmonics 0 b Z and m" harmonics a 12, 2,

f. first multiplication means for multiplying the amplitude signals and the spectral level signals;

g. means for adding the multiplied signals accumulatively for each fundamental wave and its harmonics to produce cumulative signal values H, (a X 0,) +(b b,,)+. .+(zXz,,)wherep= l, 2, m;

h. means for reading from the second memory values of the sinusoidal wave function at the respective address points PQ mod N, where Q= 0, l, N, to produce read-out signals;

. second multiplication means for multiplying the second memory read-out signals by the H, signals;

j. means for adding the multiplication products from said second multiplication means cumulatively for values of H, through l-l,, to obtain a signal in Y: H'X m QVIQD PQodN k. means for sequentially writing signal Y in an address Q in the third memory to constitute the de-' sired musical tone wave shape; and

l. means for reading out from the third memory the musical tone wave shape at a desired rate.

2. A musical tone wave shape generating apparatus as defined in claim 1 in which said means for producing digital signals representing amplitudes of a plurality of tone-colors comprise means provided for each tonecolor and producing voltage signals each having a level corresponding to each tone-color, gate circuits the output side of which are connected in common connection and which respectively receive said voltage signals, means for scanning and thereby opening these gate circuits one after another successively and repetitively at a predetermined rate and means for converting analog signals from said gate circuits to digital amplitude signals.

3. A musical tone wave shape generating apparatus as defined in claim 2 in which said means for scanning the gate circuits comprise a binary counter having a plurality of stages in cascade connection and receiving a clock pulse as their input and a decoder receiving the output of each stage of said binary counter and producing outputs corresponding to its counting successively on its output lines each of which is connected to one of said gate circuits.

4. A musical tone wave shape generating apparatus as defined in claim 3 in which said first memory is a read only memory, rows of which store the levels of spectra of the respective tone-colors and columns of which store the levels of spectra of the fundamental wave up to the highest harmonic.

5. A musical tone wave shape generating apparatus as defined in claim 4 in which said means for reading out the levels of spectra comprise means for selecting each row of said first memory in synchronization with the scanning of said gate circuits and means for select- 2 ing each column of said first memory sequentially and repetitively at each cycle of scanning of said gate circuits.

6. A musical tone wave shape generating apparatus as defined in claim 5 in which said means for selecting each column of said first memory comprise a cascade connected second binary counter which is connected in series to said binary counter first described and a decoder receiving the output of each stage of said second binary counter and producing outputs corresponding to its counting on its output lines one after another successively and cyclicly thereby to select each column of said first memory.

7. A musical tone wave shape generating apparatus as defined in claim 2 in which said means for producing the signal H comprise adding means for adding cumulatively the products of said first multiplication means and means for resetting the adding means at each cycle of scarming of said gate circuits.

8. A musical tone wave shape generating apparatus as defined in claim 6 in which said means for reading from the second memory comprise a cascade connected third binary counter having a plurality of stages connected in series to said second binary counter, a multiplier for multiplying the output 0 of said third binary counter with the output P of said second binary counter and producing an output containing a plurality of digits including the least significant digit, and a decoder receiving the output of this multiplier and oper ating in the same manner as a ring counter to produce outputs corresponding to its counting.

9. A musical tone wave shape generating apparatus as defined in claim 6 in which said means for producing the signal stage of said second binary counter. 

1. A musical tone wave shape generating apparatus comprising: a. a first memory for digitally storing the levels of the spectra of the fundamental wave and of each harmonic up to the mth harmonic of the intended tone color waves; b. a second memory for digitally storing values X0 through XN of a sinusoidal wave function at respective points of a cycle sampled by sampling number N; c. a third memory for writing incoming information to be thereafter read out; d. means for sequentially and repetitively producing digital signals (a, b, . . . z) each representing the amplitude of the respective tone color; e. means for sequentially reading out from the first memory the level of each corresponding wave spectrum of each tone color in succession at a readout rate synchronized with the rate of production of the digital signals representing the respective tone color amplitude to produce spectral level signals (fundamentals a1, b1, . . . z1; second harmonics a2, b2, . . . z2; and mth harmonics am, bm, . . . zm); f. first multiplication means for multiplying the amplitude signals and the spectral level signals; g. means for adding the multiplied signals accumulatively for each fundamental wave and its harmonics to produce cumulative signal values Hp (a X ap) + (b X bp) + . . . + (z X zp) where p 1, 2, . . . m; h. means for reading from the second memory values of the sinusoidal wave function at the respective address points PQ mod N, where Q 0, 1, . . . N, to produce read-out signals; i. second multiplication means for multiplying the second memory read-out signals by the Hp signals; j. means for adding the multiplication products from said second multiplication means cumulatively for values of H1 through Hm to obtain a signal
 2. A musical tone wave shape generating apparatus as defined in claim 1 in which said means for producing digital signals representing amplitudes of a plurality of tone-colors comprise means provided for each tone-color and producing voltage signals each having a level corresponding to each tone-color, gate circuits the output side of which are connected in common connection and which respectively receive said voltage signals, means for scanning and thereby opening these gate circuits one after another successively and repetitively at a predetermined rate and means for converting analog signals from said gate circuits to digital amplitude signals.
 3. A musical tone wave shape generating apparatus as defined in claim 2 in which said means for scanning the gate circuits comprise a binary counter having a plurality of stages in cascade connection and receiving a clock pulse as their input and a decoder receiving the output of each stage of said binary counter and producing outputs corresponding to its counting successively on its output lines each of which is connected to one of said gate circuits.
 4. A musical tone wave shape generating apparatus as defined in claim 3 in which said first memory is a read only memory, rows of which store the levels of spectra of the respective tone-colors and columns of which store the levels of spectra of the fundamental wave up to the highest harmonic.
 5. A musical tone wave shape generating apparatus as defined in claim 4 in which said means for reading out the levels of spectra comprise means for selecting each row of said first memory in synchronization with the scanning of said Gate circuits and means for selecting each column of said first memory sequentially and repetitively at each cycle of scanning of said gate circuits.
 6. A musical tone wave shape generating apparatus as defined in claim 5 in which said means for selecting each column of said first memory comprise a cascade connected second binary counter which is connected in series to said binary counter first described and a decoder receiving the output of each stage of said second binary counter and producing outputs corresponding to its counting on its output lines one after another successively and cyclicly thereby to select each column of said first memory.
 7. A musical tone wave shape generating apparatus as defined in claim 2 in which said means for producing the signal Hp comprise adding means for adding cumulatively the products of said first multiplication means and means for resetting the adding means at each cycle of scanning of said gate circuits.
 8. A musical tone wave shape generating apparatus as defined in claim 6 in which said means for reading from the second memory comprise a cascade connected third binary counter having a plurality of stages connected in series to said second binary counter, a multiplier for multiplying the output Q of said third binary counter with the output P of said second binary counter and producing an output containing a plurality of digits including the least significant digit, and a decoder receiving the output of this multiplier and operating in the same manner as a ring counter to produce outputs corresponding to its counting.
 9. A musical tone wave shape generating apparatus as defined in claim 6 in which said means for producing the signal 